A known hydrodynamic torque converter is schematically and partially illustrated in FIG. 1 and makes it possible to transmit a torque from the output shaft of an internal combustion engine in a motor vehicle, such as for instance a crankshaft 1, to a transmission input shaft 2.
The torque converter conventionally comprises an impeller wheel 3, able to hydrokinetically drive a turbine wheel 4 through a reactor 5.
The impeller wheel 3 is coupled to the crankshaft 1 and the turbine wheel 4 is coupled to guiding washers 6.
A first group of elastic members 7a, 7b of the compression spring type is mounted between the guiding washers 6 and a central hub 8 coupled to the transmission input shaft 2. The elastic members 7a, 7b of the first group are arranged in series through a phasing member 9, so that said elastic members 7a, 7b are deformed in phase with each other, with said phasing member 9 being movable relative to the guiding washers 6 and relative to the hub 8.
A second group of elastic members 7c is mounted with some clearance between the guiding washers 6 and the central hub 8 in parallel with the first group of elastic members 7a, 7b, with said elastic members 7c being adapted to be active on a limited angular range, more particularly at the end of the angular travel of the guiding washers 6 relative to the central hub 8. The angular travel, or the angular shift noted a, of the guiding washers 6 relative to the hub 8, is defined relative to a rest position (α=0) wherein no torque is transmitted through damping means formed by the above-mentioned elastic members 7a, 7b. 
The torque converter further comprises clutch means 10 adapted to transmit a torque from the crankshaft 1 to the guiding washers 6 in a determined operation phase, without any action from the impeller wheel 3 and the turbine wheel 4.
The second group of elastic members 7c makes it possible to increase the stiffness of the damping means at the end of the angular travel, i.e. for a significant a angular offset of the guiding washers 6 relative to the hub 8 (or vice versa).
It can be seen that the representation of function M=f(α) which defines the M torque transmitted though the device according to the α angular shift, comprises a first linear portion of slope Ka (for the low values of the α angular shift) and a second, more important, linear portion of slope Kb (for the high value of the α angular shift). Ka and Kb are the angular stiffness of the device, at the beginning and at the end of the angular travel respectively. If K1 defines the cumulated stiffness of the first springs of each pair of the first group, and K2 defines the cumulated stiffness of the second springs of each pair of the first group, and K3 defines the cumulated stiffness of the springs of the second group, then Ka=(K1·K2)/(K1+K2) and Kb=Ka+K3.
The break of slope between the first and second portions of the curve may generate vibrations and a significant hysteresis upon operation of the torque converter which might affect the quality of filtration obtained using the damping means.